[EricH]

I think I can help. I'm a little rusty, so I'm talking to Messrs. Beer and Johnston to brush up.

[Edit] BTW, for those that don't get the reference: That would be the statics textbook written by said authors.

I can't say that I have a solution ready to hand to you, and even if I did I'm not sure that I would. So you'll need to do a little geometry.

You actually need TWO free body diagrams. One for the arm, with a force for the cylinder coming in, and one for the cylinder itself to determine the force that the cylinder is putting in. The geometry gets messy on that one, though.

Arm diagram, sum moments around the hinge. In order to make this thing "stop", you'll need to add a moment going in the opposite direction--net result is a relationship between cylinder force, angle of arm, and distance from hinge point that the force is applied.

The fun part is when you have to figure out the applied force from the cylinder in the direction of motion, given that the cylinder is changing angles the whole time. If I'm not mistaken, that would involve knowing both distances from the arm's hinge point to the cylinder attach points (one on the arm, which is variable, and one on the support structure, which is not), and then figuring out the angle.

I think you can boil it down to one equation, too, with one variable (the angle of the arm) and several "we'll engineer these when we design the robot" numbers.